Consider the following function.procedure \textsc{M}(x)
<spanclass=′latex−bold′>if</span>0≤x≤1<spanclass=′latex−bold′>return</span>x
\qquadreturn \textsc{M}(x^2\bmod 2^{32})Let f:N→N be defined such that f(x)=0 if \textsc{M}(x) does not terminate, and otherwise f(x) equals the number of calls made to \textsc{M} during the running of \textsc{M}(x), not including the initial call. For example, f(1)=0 and f(231)=1. Compute the number of ones in the binary expansion of
f(0)+f(1)+f(2)+⋯+f(232−1).